Abstract: A valve assembly has a valve housing and a valve core body movable therewithin for providing a smooth and continuous outflow of liquid from a container, which may be unvented and rigid, through a liquid-out passageway, and provides an air-back passageway for drawing external air into the container. In a preferred embodiment, the core is rotatable within the housing by one-handed actuation. The air-back passageway is preferably a channel provided on the surface of the core body, and the liquid-out passageway is preferably provided between openings in the core body.